Abstract: Precise determinations of absolute distances such as the angular diameter distance as a function of redshifts play a crucial role in dark energy studies. There is so far only one known method to do this: Baryon Acoustic Oscillations (BAOs). Distant Type Ia supernovae give us only relative, rather than absolute, distances, as we do not know their absolute luminosities. In this talk, we present a new cosmic standard ruler: strong gravitational lensing. Roughly speaking, a measurement of the lensing time-delay of a strong lensing system tells us the physical size of the lens; thus, one can obtain the angular diameter distance to the lens by measuring angular positions of lensed images. Despite its promise, the previous studies focused only on either the time-delay or the image positions. A big advantage of this new method is that the effect of a uniform mass-sheet (i.e., external convergence) cancels out. However, a preliminary application of this method to B1608+656 and RXJ1131-1231 indicates that the inferred angular diameter distances to these systems are not as precise as one would naively guess given the precision of measurements. Our study shows that the current error budget is dominated by the uncertainties in the velocity dispersion and velocity anisotropy. The velocity anisotropy uncertainty can be reduced significantly by using the so-called "sweet-spot radius," within which the mass of the lens galaxy can be determined nearly independently of the velocity anisotropy. The success of this method has a potential for a breakthrough in dark energy studies, as the resources one needs per distance are significantly less than those required for BAO surveys.

Abstract: Statistical properties of the observed fluctuations of temperature and polarization anisotropies of the cosmic microwave background are remarkably consistent with the basic predictions of cosmic inflation driven by a single energy component. The observed fluctuations are Gaussian and adiabatic, and the strength of fluctuations weakly depends on spatial scales. The WMAP experiment has confirmed these predictions with precision, and the Planck experiment has further tightened the limits on deviations from Gaussianity and adiabaticity of fluctuations. So, has inflation really happened? We do not know yet. A definitive observational proof of inflation must come from a convincing detection of signatures of nearly-scale-invariant primordial gravitational waves generated during inflation. The so-called B-mode polarization of the cosmic microwave background is the most promising method known to date to detect such gravitational waves. In this presentation, we first briefly review the physics of E- and B-mode polarization of the cosmic microwave background. We then discuss how to measure these signals in the data in the presence of Galactic foreground and gravitational lensing. A simple analysis shows that it is possible to detect a faint B-mode signal at the level of the tensor-to-scalar ratio of 0.001, i.e., two orders of magnitude below the current limit set by the temperature anisotropy data. This is likely the smallest tensor-to-scalar ratio we would ever reach using the cosmic microwave background. Detection of nearly scale-invariant B-modes at this level or above provides a definitive proof of inflation happening at "high-scales," i.e., energy scales close to a grand unification scale, 10^{16} GeV. Finally, we comment on the recent claim of a detection of the primordial B-mode polarization by the BICEP/Keck Array collaboration.